Quantitative Methods

bureau of labor statistics want to use statistics to determine whether there is a difference between 2 countries on some measure of labor or between time periods of one country.hourly compensation in US dollars for manufacturing production workers in country A in 2015 and 2019 were $25.96 and $28.29 respectively.Hourly compensation for country B were $19.26 in 1995 and $23.89 in 2004.actual hours worked in country A in 2015 were 36.1and 35.5 in 2019.country B 37.1 in2015 and 35.9 in 2019. was the hourly labor cost higher in country A in 2019 than country B in 2019?

Quantitative Methods

Perform 6 iteration to find zero of the equation: x+3=e^x using bisection algorithm. How many steps of the algorithm are needed to compute toot of the equation?

Quantitative Methods

To approximate the value of f'''(Xk), the following formulas are used:
f'''k =[ fk+3 −3 fk+2 +3 fk+1 − fk]÷h^3
f'''k =[ fk+2 −2 fk+1 +2 fk−1 − fk−2]÷2h^3
Which formula do you find more accurate, and why?

Quantitative Methods

a) Find the interval of unit length that contains the smallest positive root of the
equation f(x) = x^3 −5x^2 +1 = 0. Starting with this interval, find an interval of
length 0.05 or less that contains the root, by Bisection method.
b) Taking the endpoints of the last interval obtained in part a) above as the initial
approximations, perform two iterations of the secant method to approximate the
root.
c) Determine the maximum error in quadratic interpolation at equispaced points.

Quantitative Methods

Set up the iteration method in matrix form for the following system of linear
equations:
3x −t = 1
4x −y + z = 4
x +2z = 1
−x −y−t = 2
Further, determine whether the method converges or not.

Quantitative Methods

Civil and transportation engineers must often estimate the future traﬃc ﬂow on roads and bridges to plan for maintenance or possible future expansion. The following data gives the number of vehicles (in millions) crossing a bridge each year for 10 years. Fit a cubic polynomial to the data and use the ﬁt to estimate the ﬂow in year 2000.
Year 1990 1991 1992 1993 1994 Vehicle ﬂow (millions) 2.1 3.4 4.5 5.3 6.2
Year 1990 1991 1992 1993 1994 Vehicle ﬂow (millions) 6.6 6.8 7 7.4 7.8

Quantitative Methods

Determine the value of the integral
I =
Z 1
0
x
p
1−x
2 dx
by composite trapezoidal rule with 3 and 5 ordinates. Improve the result by using
extrapolation technique.

Quantitative Methods

The interpolating polynomial of degree \\(\\leq n\\)with the nodes\\(x_{0}, x_{1},\\cdots, x_{n}\\) can be written as

Quantitative Methods

9.One of these describes the Lagrange’s interpolating polynomial P(x)
a.\\(p(x) = L_{1}(x)f_{0} + L_{2}(x)f_{1} + L_{3}(x)f_{2} + L_{4}(x)f_{3}\\)
b.\\(P(x) = L_{0}(x)f_{0} + L_{1}(x)f_{1} + L_{2}(x)f_{2} + L_{3}(x)f_{3}\\)
c.\\(P(x) = L_{0}(x)f_{3} + L_{1}(x)f_{2} + L_{2}(x)f_{1} + L_{3}(x)f_{0}\\)
d.\\(P(x) = L_{0}(x)f_{3} + L_{1}(x)f_{2} + L_{2}(x)f_{1} + L_{3}(x)f_{0}\\)
10.One of these is a method of solving system of linear equations:
a.Square Method
b.Inverse method
c.Lagrange Method
d.Transformation Method

Quantitative Methods

7.Iterative methods of the solutions of systems of equations are ________________
a.finite
b.sequential
c.infinite
d.non-sequential
8.Stirling\'s formula for interpolation is given by
a.\\(P_n (x) = f (x_0) + \\frac{s}{2}[df_\\frac{1}{2} + d_\\frac{-1}{2}] + \\frac{s^2}{2}d^2f_0\\)
b.\\(P_n (x) = f (x_0) + \\frac{s}{2}[df_\\frac{1}{2} + d_\\frac{-1}{2}] + \\frac{s^2}{2!}d^2f_0\\)
c.\\(P_n (x) = f (x_0) + \\frac{s - 1}{2}[df_1+ d_\\frac{-1}{2}] + \\frac{s^2}{2!}d^2f_0\\)
d.\\(P_n (x) = f (x_0) + \\frac{s}{2}[df_\\frac{1}{2} + d_\\frac{-1}{2}] + \\frac{s^2}{2!}df_0\\)